Contribution of a time-dependent metric on the dynamics of an interface between two immiscible electro-magnetically controllable Fluids

TL;DR

This paper investigates how a time-dependent surface metric affects the dynamics of a deformable interface between two magnetizable, immiscible fluids, revealing nonlinear effects and contributions to electromagnetic fields and thermodynamics.

Contribution

It introduces the role of a time-dependent surface metric into the dynamics of fluid interfaces, extending previous theories by emphasizing its nonlinear and electromagnetic effects.

Findings

Nonlinear surface dynamical equations with mean curvature term

Modified electromagnetic fields and charge densities at the interface

Enhanced understanding of thermodynamic fluxes at the interface

Abstract

We consider the case of a deformable material interface between two immiscible moving media, both of them being magnetiable. The time dependence of the metric at the interface introduces a non linear term, proportional to the mean curvature, in the surface dynamical equations of mass momentum and angular momentum. We take into account the effects of that term also in the singular magnetic and electric fields inside the interface which lead to the existence of currents and charges densities through the interface, from the derivation of the Maxwell equations inside both bulks and the interface. Also, we give the expression for the entropy production and of the different thermo-dynamical fluxes. Our results enlarge previous results from other theories where the specific role of the time dependent surface metric was insufficiently stressed.